Certain types of structural elements, like riveted or rolled beams and girders, etc., of older steels, often have tapered flanges and the steels themselves are as a rule mor or less inhomogeneous. The fracture toughness at in-plane loading of related structural details, has been observed to vary significantly in the thickness direction and generally increases outwardly from the mid-section part. The most common fracture toughness test specimen used for testing of samples taken from oldes steel structures, in e.g. assessment work, is the three point bend specimen. This specimen, like all standard specimen types, is plane-parallel and if machined from a tapered part it will not necessarily yield a fair estimate of the effective fracture toughness for a through crack in situations where fracture toughness varies across the thickness. In view of this, a modified three point bend specimen with partly tapered sides has been designed so as to accomodate samples with this feature. The project includes calibration , testing and evalutation of the modified specimen. The firt part of the project, which is reported here, is mainly analytical and is aimed at obtaining a first and rough estimate of the order of influence the modified geometry upon crack tip parameters.